How to optimize neural network parameters with REINFORCE
The term REINFORCE actually corresponds to a method of estimating gradients, it is not particular to reinforcement learning. The paper you linked doesn't appear to deal with RL at all, so the issue they're describing is not one that you should expect to find in a policy gradient application.
If you're using REINFORCE to estimate policy gradients in RL (this is the common use case), your parameters are parameterizing a policy function. The inputs are states and the outputs are actions. The issue with estimating the gradient of the parameters is as follows. In RL the objective is to maximize expected rewards. This is an expectation with respect to the policy of the cumulative reward of a trajectory. If you take the gradient of this wrt the parameters, since the expectation is wrt the policy which depends on the parameters, you can't move the gradient inside the expectation so you can't estimate the gradient from samples. Using REINFORCE however, you use the &quot;log-derivative&quot; trick to rewrite the objective as an expected gradient, which can be estimated from samples.